Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| isoclinism | isoclinic class of C3⋊D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C3×C7 |
| direct product | C72×C3⋊D57 |
| unambiguous semidirect product | C3⋊(C72×D57) |
| unambiguous semidirect product | C19⋊(C72×C3⋊D3) |
| Fitting, socle, Hall | C32×C72×C19 ⋊ C2 |
| derived, Hall | C32×C19 ⋊ C2×C72 |
| Hall | C72×C19 ⋊ C3⋊D3 |
| Hall | C32×C72 ⋊ D19 |
| Sylow | C19 ⋊ C72×C3⋊D3 |
| Sylow | C32 ⋊ C72×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C3⋊D57 |
| commutator, cosocle, hypocenter | C32×C19 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C19 | C2 |
| LCS | G ▷ C32×C19 | |
| UCS | C1 ◁ C72 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8379 |
4263 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C72×D57, C7×D21⋊D57, #45692724, … |
| maximal normal subgroup of | D3×C72×D57, C7×D21⋊D57, #45692724, … |
| maximal quotient of | C72×C3⋊Dic57, C2×C72×C3⋊D57 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 406);